Shirts cost $25, pants cost $40, and sweaters cost $65.

Let x represent the cost of a shirt. Let y represent the cost of a pair of pants. Let z represent the cost of a sweater.

Sarah buys two shirts, one pair of pants, and one sweater. So 2x + y + z = 155

Cindy purchases one shirt, two pairs of pants, and two sweaters. So x + 2y + 2z = 235.

Gina buys three shirts and four pairs of pants. So 3x + 4y = 235.

Since we have two equations that equal 235 and one of those equations does not contain the variable z we will first solve for z.
x + 2y + 2z = 3x + 4y
2y + 2z = 2x + 4y
2z = 2x + 2y
z = x + y

Using the above value of z and knowing that 3x = 235 - 4y (from the third equation) we will solve for y in the first equation.
2x + y + z = 155
2x + y + (x + y) = 155
3x + 2y = 155
(235 - 4y) + 2y = 155
235 - 2y = 155
-2y = -80
y = 40

Now solve for x.
3x + 4y = 235
3x + 4(40) = 235
3x + 160 = 235
3x = 75
x = 25

Now solve for z.
z = x + y
z = 25 + 40
z = 65

 

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